Herb Gross defines the meaning and terminology of the mathematical concepts sets, functions and graphs. Functions are defined as the program in a process that takes an input, follows the program (rules) and produces an output. In this context, arithmetic is likened to knowing the input and program and determining the output; algebra is compared to knowing the output and the program and determining the input; finally Analytic Geometry is comparable to determining the function when you know the graph (that is, the ordered pair of input and output). This material and much more is also available online at www.adjectivenounmath.com.
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